Yes, that can be done. You have the right idea: pass the brand name as a key/value pair.
If you are using the PDO extension, you might write something like:
while ($row = $stmt->fetch(PDO::FETCH_ASSOC)) {
echo '<a href="brand.php?brand="' . urlencode($row['brand']) . '">'
. htmlspecialchars($row['brand']) . "</a><br />\n";
}
You can adapt this for say, MySQLi, quite easily.
The [man]urlencode/man and [man]htmlspecialchars/man should be used to escape the data in the URL and the text respectively.
In brand.php, you would check $_GET['brand'] and then retrieve from the database using its value.